The last lesson on normal distribution helped quantify volatility and give investors a platform with which they can assess risk. However, the theory fails to address events in which the dispersion of data moves far away from the mean (average). As investors have experienced throughout time, the stock market is prone to market crashes, which are known as “fat tail” events. These are events in which price skews towards extreme ends of the distribution curve.
Fat tail events, as described by the normal distribution theory, occur once every 7,000 years. The reality however is that they occur much more often. Using the past as a reference, we can declare that fat tail events happen roughly one to two times per decade.
The problem is further enhanced by the fact that these events are not addressed correctly by the Black-Scholes pricing model, which assumes that implied volatility is the same for every strike price in the same expiration month. This is not true though- implied volatility varies among different strikes. This becomes apparent when we look at a volatility graph:
The graph above displays the typical volatility skew of an underlying stock’s option contracts. Implied volatility is priced in much higher as the underlying stock price declines. The reason for this would be that if there was a market crash, investors who owned the underlying stock would rush out to purchase put options for protection. Also, deep ITM call options exhibit one-for-one price movement with the underlying stock (1.00 delta), meaning investors can use deep ITM options to profit the same as stocks would while allocating much less capital than owning 100 shares. Accordingly, as the underlying stock increases in value, volatility decreases because traders associate rising markets with stable markets.
Here is a real-life example:
Another pattern exhibited by graphing volatility is known as the volatility smile, which is shown below:
The volatility smile, while less common, will generally appear when there is less time until expiration. The pattern suggests that implied volatility is higher for OTM and ITM options compared to ATM options. The reason would most likely derive from the fact that investors are expecting a large move in the underlying stock. Because of this, option buyers become willing to pay more for the option contracts. Here is another real-life example:
The volatility smile will generally cause OTM put and ITM call options to be overpriced and OTM call and ITM put options to be under priced.
Investors need to identify the volatility skews that are present on the underlying strike prices before they open a position.
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